关于上半平面的静态纳维-斯托克斯方程

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2024-02-05 DOI:10.1007/s10440-024-00636-3

Adrian D. Calderon, Van Le, Tuoc Phan

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引用次数: 0

摘要

我们研究了上半平面不可压缩的静态 Navier-Stokes 方程，该方程具有同质 Dirichlet 边界条件和非零外力作用项。在适当的外力条件下，证明了弱解的存在性。此外，还给出了基于弱解无穷大处各种增长条件的弱-强唯一性准则。这是通过使用能量估计和哈代不等式实现的。对流函数进行了若干估计，并证明了 2 维空间上同质 Sobolev 空间的两个具有适当权重的密度定理。

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On Stationary Navier-Stokes Equations in the Upper-Half Plane

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy’s inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2-dimensional space are proved.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.